TOMS552
Constrained Overdetermined Linear Systems in L1.

TOMS552 is a FORTRAN90 library which computes a solution of an overdetermined constrained linear system, minimizing the error in the L1 norm.

TOMS552 is an implementation of ACM TOMS algorithm 552.

The overdetermined linear system being solved is

A * X = B.

The equality constraints have the form:

C * X = D

and the inequality constraints have the form:

E * X >= F.

The program is required to seek a solution X which satisfies the constraints, and which minimizes the L1 norm (sum of absolute values of components) of A*X-B.

The original, true, correct version of ACM TOMS 552 is available in the TOMS subdirectory of the NETLIB web site.

Languages:

TOMS552 is available in a FORTRAN90 version.

Author:

Ian Barrodale,
Frank Roberts.

Reference:

Ian Barrodale, Frank Roberts,
Algorithm 552: Solution of the Constrained L1 Approximation Problem,
ACM Transactions on Mathematical Software,
Volume 6, Number 2, March 1980, pages 231-235.
Helmuth Spaeth,
Mathematical Algorithms for Linear Regression,
Academic Press, 1991,
ISBN: 0-12-656460-4,
LC: QA278.2.S6313.

Source Code:

toms552.f90, the source code.

Examples and Tests:

toms552_test.f90, a sample calling program.
toms552_test_input.txt, an input file for use with the sample program.
toms552_test.txt, the output from a run of the sample program.

List of Routines:

CL1 solves a linear programming problem.
COL adds a multiple of vector V2 to vector V1.
L1ORTH carries out orthogonal regression for the L1 norm.
TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.

Last revised on 28 December 2007.